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We consider a degradation model which is the sum of two independent processes: an homogeneous gamma process and a Brownian motion. This model is called perturbed gamma process. Based on independent copies of the perturbed gamma process observed at irregular instants we propose to estimate the unknown parameters of the model using the moment method. Some general conditions allow to derive the asymptotic behavior of the estimators. We also show that these general conditions are fulfilled for some specific observation schemes. Finally, we illustrate our method by a numerical study and an application to a real data set. [ABSTRACT FROM AUTHOR]

The nonparametric estimation of the Bernoulli regression function is studied. The uniform consistency conditions are established and the limit theorems are proved for continuous functionals onC[a, 1 − a], 0 < a < 1/2. [ABSTRACT FROM AUTHOR]